cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A367490 Expansion of e.g.f. -x * log(4 - 3*exp(x)).

Original entry on oeis.org

0, 0, 6, 36, 336, 4380, 73080, 1481844, 35320992, 966875724, 29874822600, 1028081942052, 38985534525168, 1614899447153148, 72543518616692760, 3512306387815898580, 182320857226312198464, 10100520471366488756652, 594804877105749056467560
Offset: 0

Views

Author

Seiichi Manyama, Nov 19 2023

Keywords

Crossrefs

Programs

  • PARI
    a(n) = n*sum(k=1, n-1, 3^k*(k-1)!*stirling(n-1, k, 2));

Formula

a(n) = n * Sum_{k=1..n-1} 3^k * (k-1)! * Stirling2(n-1,k).

A367486 Expansion of e.g.f. 1/(3 - 2*exp(x))^x.

Original entry on oeis.org

1, 0, 4, 18, 168, 1830, 24540, 388122, 7084560, 146650446, 3395460900, 86962122786, 2441210321880, 74542218945558, 2459830123779756, 87236196407090730, 3308881779086345760, 133667058288336876894, 5729380391745420070068
Offset: 0

Views

Author

Seiichi Manyama, Nov 19 2023

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, 2^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A367489(k) * binomial(n-1,k-1) * a(n-k).

A367485 Expansion of e.g.f. 1/(3 - 2*exp(x))^(x/2).

Original entry on oeis.org

1, 0, 2, 9, 72, 735, 9300, 140511, 2469600, 49509711, 1115030220, 27871094823, 765622756800, 22925878253031, 743201185847484, 25930679953675815, 968847417413563200, 38593990513290611967, 1632776110278839747532, 73111823927074777887111
Offset: 0

Views

Author

Seiichi Manyama, Nov 19 2023

Keywords

Crossrefs

Programs

  • Mathematica
    With[{nn=20},CoefficientList[Series[1/(3-2Exp[x])^(x/2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Dec 29 2024 *)
  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, 2^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])/2); v;

Formula

a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A367489(k) * binomial(n-1,k-1) * a(n-k).
Showing 1-3 of 3 results.